1. Field of the Invention
This invention relates to a method for monitoring and controlling a chemical process essentially instantaneously based on real time measurements of the concentration of reactants or products produced by the process, or both.
2. Background Discussion
There are many chemical processes which require physical parameters to be altered based on the concentration of reactants in the process or products produced by the process. Frequently, temperatures, pressures, flow rates, pH and other physical parameters of the process must be changed to optimize the operation of the process. (As used herein chemical process(es) shall mean any process wherein the concentration of reactants or products produced by the processes changes. It includes in vitro and in vivo biochemical, nuclear, metallurgical, petrochemical, etc, processes.)
Conventional monitoring and control techniques are unable to measure the concentration of reactants, the products produced by the process, or both, with sufficient speed to then regulate process parameters based on the measured concentrations. One technique used to measure the concentration of reactants is electromagnetic radiation absorption technology. Over the range of the electromagnetic spectrum, all chemicals absorb or reflect "light" in a unique way that is characteristic of the structure of chemical being examined and its concentration in a mixture of different chemicals. For our purposes, light includes all regions of the electromagnetic spectrum from x-rays, UV, visible, infrared to microwaves. For example, one may determine the concentration of sucrose in water by spectroscopy, a technology wherein, for example, an aqueous sucrose solution is exposed to infrared light (IR) at different, discrete wavelengths.
The absorption spectra (the level of light absorption over a range of different, discrete wavelengths of light) is characteristic of the aqueous sucrose solution. The spectra is usually described in terms of the wavelength of electromagnetic radiation, for example, from 1 to 100 micrometers (.mu.m). In spectroscopy, one frequently finds it useful to use a slightly different measure for the spectral position known as the wavenumber. The wavenumber, in cm.sup.-1, is related to the wavelength in .mu.m by 1/10,000, that is 1 .mu.m is 10,000 cm.sup.-1 and 10 .mu.m is 1,000 cm.sup.-1. Conventional Fourier Transform-IR technology is routinely capable of scanning from 1.2 .mu.m to 100 .mu.m in as little as 1/8 second with a resolution of 2.5.times.10.sup.-5 .mu.m (0.25 cm.sup.-1). For most purposes, including the purposes of the present invention (on-line chemical control and monitoring), a resolution of 2.0-4.0 cm and scan speed of 1-10 seconds is sufficient. This allows use of less expensive equipment since one pays a premium for speed and resolution.
The governing principle behind current quantitative analytical methods of transmission or absorption measurement instruments, in which realm IR analysis falls, relies on a relationship known as the Bouguer-Beer-Lambert Law. Many sources simply call this Beer's Law. In the simplest form it is written: EQU A=abc [1]
where A is the absorbance, a is the molar absorptivity, b is the pathlength, and c is the concentration. Since the amount of energy absorbed is related to the number of molecules, the concentrations involved are molar quantities such as moles per liter or mole fraction. A mole of a material is a fixed number of molecules, e.g., 6.023.times.10.sup.23 if the weight (called the molecular weight in this case) is given in grams. The molar absorptivity is the absorbance expected when 1 mole of a particular compound is present at the particular wavelength that the measurement is made.
Equation [1] is normally assumed to hold for every discrete wavelength for which the instrument can distinguish adjacent wavelength intervals. For example, with a 2.0 cm.sup.-1 resolution, it is possible to distinguish reproducible differences as close as 1.0 cm.sup.-1. Thus, a spectra from 450 cm.sup.-1 to 4400 cm.sup.-1 would have 3,951 points and equation [1] would be assumed to apply to each of these points.
It is frequently useful to combine terms in equation [1] into the form: EQU A=kc [2]
where k now represents a "constant" which combines the molar absorptivity and the pathlength. By measuring the absorbance, A, of samples with differing amounts of material at various concentrations, c, one can calculate k. When k does not vary over a range of concentrations, the samples and the material being measured are said to obey Beer's Law.
Once k is known, unknown samples of the material are determined simply by measuring the Absorbance, A, and dividing by k for each discrete wavelength for which the measurements are made and for which Beer's Law has been shown to apply.
One can measure transmission as well as absorbance. The two quantities are related by the expression: EQU A=ln(1/T) [2]
where T is transmission. The transmission is defined as the fractional reduction in intensity of a beam of electromagnetic radiation passing through the medium containing the absorbing material. Formally, it is: EQU T=I/I.sub.0 [ 4]
where I is the measured intensity with the absorbing material in the beam and I.sub.0 is the measured intensity without the absorbing material. Sometimes Beer's Law is written: EQU I=I.sub.0 e.sup.-abc [ 5]
which is the algebraic combination of equations [1], 3] and [4]. It is much more convenient to analyze results using equations [1] avoiding the use of exponentials.
When one has a mixture of materials, equations [1] or [2] is usually held to be applicable to each of the materials separately. That is, for a mixture of 3 materials at each wavelength or wavenumber: EQU A=k.sub.1 c.sub.1 +k.sub.2 c.sub.2 +k.sub.3 c.sub.3 [ 6]
where the subscripts refer to the three components. Since equation [6] holds at each wavelength (or wavenumber), there are as many equations as wavelengths so the values at the selected wavelength (m) can be written as A.sub.m =k.sub.m1c1 +k.sub.m2c2 +k.sub.m3c3. This could be, for example, a mixture of three gases moving through a gas cell attached to an FT-IR instrument or two solutes (such as sucrose and ethanol) dissolved in a solvent (such as water). In current practice, again assuming that Beer'Law is valid, the k.sub.1 would have been determined from previous experiments and thus the c.sub.1 can be calculated if three sets of measurements are taken at three or more wavelengths. In current practice, the measurements over many wavelengths are used to find the "best fit" for c.sub.1 using least squares or partial least squares regression analysis. There is no way of determining which series or ranges of wavenumbers is the best to use. This is done exclusively by trial and error based on the analyst's experience.
For a discussion of the state-of-the-art, the book "Fourier Transform Infrared Spectrometry" by Peter R. Griffiths and James A. de Haseth, John Wiley & Sons, 1986 is recommended. Chapter 10 in this book discusses quantitative analysis. Of particular importance is section IV on multicomponent analysis beginning on page 355. On page 356, the authors note that Beer's Law is a requirement for the analysis techniques they present.
There is also a four volume series edited by John R. Ferraro and Louis J. Basile. The series is entitled "Fourier Transform Infrared Spectroscopy" and is published by Academic Press, Inc. Volume 1 was published in 1978, Volume 2 in 1979, Volume 3 in 1982, and Volume 4 in 1985. The latest volume contains a contribution by P. C. Gillette, J. B. Lando and J. L. Koenig on "A Survey of Infrared Spectral Processing Techniques." They again state the requirements for Beer's Law as well as mention that least squares analysis is a preferred technique. Based on experimentation in connection with conducting chemical analysis which the present invention addresses successfully, the least squares and related techniques are highly overrated and are rarely the best techniques for looking at variable data or determining the "best fit" in analysis of spectral data. Further, Beer's Law rarely holds in practical systems, particularly in solvent systems or complex mixed gases or polymeric solids.